I watched Gilbert Strang's video lectures on linear algebra (the MIT freshman course) for preparation for my PhD qualifier exam, and as a third year grad student, I could appreciate the relevance of almost every single topic in the class. That is, seven years after freshman linear algebra and with countless applications programmed, papers read and implemented, and theoretical/applied classes taken, it "all made sense" (don't ask me what a freshman is supposed to make of that material, other than to acquire it at a very abstract superficial level).

The early classes are the prerequisites for every and anything you might wind up doing with math. Including becoming a math prof, or a web dev, or dropping out. Nobody tells you, for every section of every textbook you have to read, what its myriad applications might be, and you can't get a customized build of just the topics you want.

But we're all startup people here right? Can this shortcoming be fixed? Can we make a detailed dependency graph of topics in applied mathematics, which could potentially be used to generate custom learning builds?

I use it every single day. In the past I did all kinds of simulations for avionics and flight. I've used it for epidemiology studies, signal processing, augmented reality, machine vision for factories, and nowadays I'm using it in computer vision. I couldn't get anywhere without differential equations, linear algebra, and so on.

Discrete mathematics includes graph theory, discrete statistics, topology, OR, and so on.

College isn't meant to be votech. It's meant to expand your horizons. How would you go off and build a robot, write code for the NIH, work for a VR firm, write code for oil&gas exploration, program a drone if you didn't know this math? My only regret is that I didn't take more math.

I guess it is all taste, but I want the ability to just go and do what I want, and frankly, this sort of work is deeply interesting because it requires you to solve interesting problems. By that I mean that learning the API to Qt or Unity or something is not deeply interesting - it difficult to the extent that it is opaque/poorly documented. Once you learn the pattern to put something together in those frameworks the work becomes quite pedestrian (can you put a button here that ... yes, I can do that, yawn).

Sure. I work in ML, in industry. Singular value decomposition and related methods are huge. Understanding basis vectors. Most of the notation I use every day. The intuitive understanding of linear algebra and ability to read papers that rely on it. a lot of ML relies on understanding data as points in high dimensional space.

a lot of the stuff you're mentioning is required for what I'd consider the really interesting topics in CS, stuff like ML, operations research, scientific computing.

I've used differential equations building a physics-based optimization system for an industrial process. Symbolically solving parts of the system really increased its accuracy and stability.